The authors nd necessary and suucient conditions for GDT weighted Marcinkiewicz inequalities based at Stieltjes zeros.

Marcinkiewicz-Zygmund Inequalities involving the zeros {xkn} of Jacobi polynomials for the weight wα,β can take the form

The boundedness for the multilinear Marcinkiewicz operators on certain Hardy and Herz-Hardy spaces are obtained.

We consider order and type properties of Marcinkiewicz and Lorentz function spaces.We show that if 0 < p < 1, a p-normable quasi-Banach space is natural (i.e. embeds into a q-convex quasi-Banach lattice for some q > 0) if and only if it is finitely representable in the space Lp,∞. We also show in particular that the weak Lorentz space L1,∞ do not have type 1, while a non-normable Lorentz space ...

This paper studies the bifurcations of exact solutions for time–space fractional complex Ginzburg–Landau equation with parabolic law nonlinearity. Interestingly, different parameters, there are kinds first integrals corresponding traveling wave systems. Using method dynamical systems, which is from previous works, we obtain phase portraits In addition, derive parametric representations solitary...

We investigate, by “ à la Marcinkiewicz” techniques applied to the (asymptotic) density function, how dense systems of equal spheres of Rn, n ≥ 1, can be partitioned at infinity in order to allow the computation of their density as a true limit and not a limsup. The density of a packing of equal balls is the norm 1 of the characteristic function of the systems of balls in the sense of Marcinkie...

In this paper, the high-frequency diffraction of a plane wave incident along planar boundary turning into smooth convex contour, so that curvature undergoes jump, is asymptotically analysed. An approach modifying Fock parabolic-equation method developed. Asymptotic formulas for wavefield in illuminated area, shadow, and penumbra are derived. The penumbral field characterized by novel previously...